Related papers: Geometric Phase and Chiral Anomaly in Path Integra…
A wave function picks up, in addition to the dynamic phase, the geometric (Berry) phase when traversing adiabatically a closed cycle in parameter space. We develop a general multidimensional theory of the geometric phase for (double) cycles…
The Aharonov-Anandan phase is introduced from a physical point of view. Without reference to any dynamical equation, this phase is formulated by defining an appropriate connection on a specific fibre bundle. The holonomy element gives the…
The level crossing problem is neatly formulated by the second quantized formulation, which exhibits a hidden local gauge symmetry. The analysis of geometric phases is reduced to a simple diagonalization of the Hamiltonian. If one…
Construction of skeletonized path integrals for a particle moving on a curved spatial manifold is considered. As shown by DeWitt, Kuchar and others, while the skeletonized configuration space action can be written unambiguously as a sum of…
The problem of geometric phase for an open quantum system is reinvestigated in a unifying approach. Two of existing methods to define geometric phase, one by Uhlmann's approach and the other by kinematic approach, which have been considered…
The normalization in the path integral approach to quantum field theory, in contrast with statistical field theory, can contain physical information. The main claim of this paper is that the inner product on the space of field…
Study of symmetry, topology and geometric phase can reveal many new and interesting results on the topological states of matter. Here we present a completely new and interesting result of symmetry, topology and quantization of geometric…
The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection…
The dielectric property $(2\times2)$ of the anisotropic optical medium is found out considering the polarized photon as two component spinor of spherical harmonics.The Geometric Phase of single polarized photon has been evaluated in two…
An adiabatic change of parameters along a closed path may interchange the (quasi-)eigenenergies and eigenspaces of a closed quantum system. Such discrepancies induced by adiabatic cycles are refereed to as the exotic quantum holonomy, which…
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to…
Geometric phases play a crucial role in diverse fields. In chemistry they appear when a reaction path encircles an intersection between adiabatic potential energy surfaces and the molecular wavefunction experiences quantum-mechanical…
A quantal system in an eigenstate, of operators with a continuous nondegenerate eigenvalue spectrum, slowly transported round a circuit C by varing parameters in its Hamiltonian, will acquire a generalized geometrical phase factor. An…
A convenient framework is developed to generalize Berry's investigation of the adiabatic geometrical phase for a classical relativistic charged scalar field in a curved background spacetime which is minimally coupled to electromagnetism and…
The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wavefunction and a recently proposed quantum hydrodynamical description of its dynamics. An…
We study characteristic aspects of the geometric phase which is associated with the generalized coherent states. This is determined by special orbits in the parameter space defining the coherent state, which is obtained as a solution of the…
By considering the most general metric which can occur on a contractable two dimensional symplectic manifold, we find the most general Hamiltonians on a two dimensional phase space to which equivariant localization formulas for the…
Geometric phases accompanying adiabatic processes in quantum systems can be utilized as unitary gates for quantum computation. Optimization of control of the adiabatic process naturally leads to the isoholonomic problem. The isoholonomic…
We show that the adiabatic approximation for nonselfadjoint hamiltonians seems to induce two non-equal expressions for the geometric phase. The first one is related to the spectral projector involved in the adiabatic theorem, the other one…
Geometric measure of entanglement and geometric phase have recently been used to analyze quantum phase transition in the XY spin chain. We unify these two approaches by showing that the geometric entanglement and the geometric phase are…